Related papers: Group ring cryptography
The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…
We consider a problem, which we call secure grouping, of dividing a number of parties into some subsets (groups) in the following manner: Each party has to know the other members of his/her group, while he/she may not know anything about…
We propose public-key cryptosystems with public key a system of polynomial equations, algebraic or differential, and private key a single polynomial or a small-size ideal. We set up probabilistic encryption, signature, and signcryption…
A cryptographic protocol (CP) is a distributed algorithm designed to provide a secure communication in an insecure environment. CPs are used, for example, in electronic payments, electronic voting procedures, database access systems, etc.…
Cryptography is the study of methods of sending messages in disguised form so that only the intended recipients can remove the disguise and read the messages. Information security has become a very critical aspect of modern communication…
Let $R$ be an associative ring with identity and let $N$ be a nil ideal of $R$. It is shown that units of $R/N$ can be lifted to units in $R$. Under some mild conditions on the ring, a procedure is given to determine those lifted units in a…
This paper introduces and studies the higher-order group inverse in a ring. We extend known properties of the higher-order group inverse from complex matrices to elements of a ring and, in the process, derive new results. We further…
An information is a message which is received and understood. Information can be sent one person to another over a long range but the process of sending information must be done in a secure way especially in case of a private message.…
We study codes with a single check element derived from group rings, namely, checkable codes. The notion of a code-checkable group ring is introduced. Necessary and sufficient conditions for a group ring to be code-checkable are given in…
It has been found that an algorithm can generate true random numbers on classical computer. The algorithm can be used to generate unbreakable message PIN (personal identification number) and password.
We believe that there is no real data protection without our own tools. Therefore, our permanent aim is to have more of our own codes. In order to achieve that, it is necessary that a lot of young researchers become interested in…
We consider an application to the discrete log problem using completely regular semigroups which may provide a more secure symmetric cryptosystem than the classic system based on groups. In particular we describe a scheme that would appear…
The combination of the group ring setting with the methods of character theory allows an elegant and powerful analysis of various combinatorial structures, via their character sums. These combinatorial structures include difference sets,…
This paper introduces a newly developed private key cryptosystem and a public key cryptosystem. In the first one, each letter is encrypted with a different key. Therefore, it is a kind of a one-time pad. The second one is inspired by the…
The purpose of the paper is to give new key agreement protocols (a multi-party extension of the protocol due to Anshel-Anshel-Goldfeld and a generalization of the Diffie-Hellman protocol from abelian to solvable groups) and a new…
It has been suggested that the algebraic structure of AES (and other similar block ciphers) could lead to a weakness exploitable in new attacks. In this paper, we use the algebraic structure of AES-like ciphers to construct a cipher…
Encrypted control is a promising method for the secure outsourcing of controller computation to a public cloud. However, a feasible method for security proofs of control has not yet been developed in the field of encrypted control systems.…
One of the possible generalizations of the discrete logarithm problem to arbitrary groups is the so-called conjugacy search problem (sometimes erroneously called just the conjugacy problem): given two elements a, b of a group G and the…
Neural cryptography is based on a competition between attractive and repulsive stochastic forces. A feedback mechanism is added to neural cryptography which increases the repulsive forces. Using numerical simulations and an analytic…
Given a cryptographic group action, we show that the Group Action Inverse Problem (GAIP) and other related problems cannot be NP-hard unless the Polynomial Hierarchy collapses. We show this via random self-reductions and the design of…